Peace lilies can be a little tricky to take care of. I brought one home from my step-daughter's funeral and wanted badly to keep it alive. Through trial and error, I finally discovered what it wants. I keep it in a cool room (temp around 65-70), don't water too much (only about every week and a half during summer, every two weeks in winter) and it only gets bright light, no direct sun. This treatment stopped the browning tips on the leaves and it's growing and blooming beautifully now. Hope this helps.
In a very high % of cases, necrotic leaf tips & margins are symptomatic of over-watering and/or a high level of solubles in the soil, both of which are often related to a soil that is too water retentive and force you to water in sips, a practice that ensures salt build-up in the soil. The lower humidity levels of winter, though not directly responsible for the unsightly foliage, are a contributory factor that worsen the effects of compromised root function.
Changing to a soil that allows you to water properly without concern that your soil will remain saturated for extended periods and allow root rot to set in, is the best way to address/correct the problem. Roots are the heart of the plant, and your plant can NEVER be all it CAN be unless you are able to provide an environment that ensures a healthy root system.
The sticky thread at the top of this forum should offer some additional insights you might find helpful.
I also wonder if your pot has a drainage hole? It looks like the sort that sometimes doesn't have drainage, and that will greatly increase the chances that you'll overwater the plant and will also contribute to the issues that Al mentioned around salt buildup.
I would have to say that if your mom has a really nice peace lily, it's much more likely that it's nice in spite of the coffee grounds rather than because of them. Forum discussions frequently center on the question of whether or not it's a good idea to add dilute coffee/tea or grounds to plants as a 'tonic', but Arabica (coffee) and Camellia (tea) are known for their toxic alkaloid (caffeine) content and their allelopathic affect on plants as well as autotoxic (poison to their own seedlings) effects on future generations. Caffeine interferes with root development by impairing protein metabolism. This affects activity of an important bio-compound (PPO) and lignification (the process of becoming woody), crucial steps for root formation.
We also know that the tannins in both coffee and tea are known allelopaths (growth inhibitors). There are ongoing experiments to develop herbicides using extracts from both coffee and tea that cause me to want to say they might serve better as a nonselective herbicide than as a tonic. I would not use either (stale coffee or tea) by applying directly to my plants - especially containerized plants; nor would I add tea bags/coffee grounds to my container soils.
Al thanks so much for your input and expertise! I had no idea of the things you said, I am very glad to know about the negative effects of both coffee and tea. I will pass this information on to my mom, too!